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There is something going on that is incredibly suspicious if you are fighting ANYTHING in that level range with such a high amount of armor class. If your GM was modifying your to hit based on severe winds, that might explain SOME of the difference but 48 still seems way too high.
Dragon's tend to have one fairly glaring weakness. Touch AC. If you can find a way to target that (most often with spells), you can generally guarantee a hit on them provided there is no concealment hindering you. Touch AC generally means spells, and you have to deal with spell resistances and/or saving throws. A Magus has ways of turning their melee attacks into touch attacks for a round at a time.
What sources are you allowed?
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Okay, I thought this sounded vaguely familiar: https://paizo.com/threads/rzs43le3?Build-help-Magic-missle-user-Level-7-To- 12
If you are still facing ACs that high, just quit the campaign: There ain't nothing in the game that will help you hit AC's / SR's that high...
48+ AC is average for CR, umm [looks at the bottom of the chart], 30... CR 30 critters average an AC of 48. That is closer to double what you "should" be seeing at your level, or at least time and a half. To say something is not right is a gross understatement.
There is a Paladin built for dragonslaying... Oath Aginst the Wyrm. It's not the best, but you could probably make it work. Not sure what you really want to do other than knight with a sword.
At level 13+, a Magus can use Spell Blending Arcana to pick up Touch of Gracelessness and Calcific Touch. Lol. And if you were interested in giving archery another try, an Eldritch Archer Magus [with Reach Spellstrike and Distant Spellstrike] could fire both of these spells attached to arrows, using the bow's range instead of the spells' range(s). The idea is to try land Touch of Gracelessness to drop the dragon's already low Dex [and drop its already low fly maneuverability], then tag it with Calcific Touch to petrify it... game over, man, game over.
I'm just adding another comment here... A Great Wyrm Gold Dragon with Mage Armor and Shield cast on itself can have an AC of 48. And a touch AC of 8. It has spell resistance of 34. You should NOT be fighting anything near that level (CR23). Not around level 11.
Hell, I run a fairly powered up Mythic game, and my players are level 12 with 6 mythic tiers. They aren't even fighting something like that.
Sounds like you have a GM on a power trip who wants to beat the players (pro tip, the GM always win if they want, its more a question of will the players accept the way its done and continue playing).
Under no circumstances should a party of level 11 be facing such a high level enemy. Don't get me wrong, I've GM'd for party with high level of system mastery, and I've gone as high as CR +5/6 to get an enemy of sufficient challenge to the party (regularly using CR+3 enemies as minion) but this is insane.
If the enemy is strong to the point where you're only succeeding on rolls of 18+, you have to stop and ask the GM what's going on here. Do they actually intend for you to be able to win the fight? It doesn't sound like it. Do they intend for you to negotiate with the dragon? Maybe. Do they intend for you to be beaten and become servants of the dragon? Quite possibly. If your GM does want to have a plot railroad like becoming the dragons minions, it would better if the GM simply told you "This dragon completely outclasses you, you will lose this fight but the dragon does not kill you. Instead it collects you and uses magic to compel you to do his bidding."
If you're building an encounter (as a GM) in such a way that the only reasonable outcome is the NPC winning, you should instead stop and not pretend that the players can affect anything. It's a waste of your time and theirs. Instead tell the players what's going to happen. It generally helps if you get their buy in on it too.
I would not be so quick to judge the GM. Without knowing the details of the campaign, it is impossible to tell if the encounter is too tough. The original post is asking for advice for a character between 11th and 15th level. That is the only detail that was provided. We don’t know what the point buy is or if the campaign is using mythic rules. I ran a mythic campaign where the characters got to 15th level and 5 mythic tiers. The paladin in that group could get 4 attacks per round all at +34 to hit (Multiple mythic path abilities precision) doing 2d4 +45 with a 15-20 critical range and a x3 multiple. Now this is after being fully buffed by mythic spells and under inspired rage. This character is within the level ranged specified.
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I would not be so quick to judge the GM. Without knowing the details of the campaign, it is impossible to tell if the encounter is too tough. The original post is asking for advice for a character between 11th and 15th level. That is the only detail that was provided. We don’t know what the point buy is or if the campaign is using mythic rules. I ran a mythic campaign where the characters got to 15th level and 5 mythic tiers. The paladin in that group could get 4 attacks per round all at +34 to hit (Multiple mythic path abilities precision) doing 2d4 +45 with a 15-20 critical range and a x3 multiple. Now this is after being fully buffed by mythic spells and under inspired rage. This character is within the level ranged specified.
Check the thread I linked back in post #3 or so: Same OP, same issue, slightly lower level from about 6 months ago. The OP also had a 'insanely high SR' thread from about the same period (which I linked in the thread I linked).
There is a distinct lack of details on this campaign(s), but the OP does seem to have a 'I miss when I rolled a 19' issue. Most notably, I don't recall seeing anything on how the other members of the party were handling the situation, which might give us a clue on what is actually going on*...
Facing an APL+10ish dragon without a TPK seems unlikely without a volume of house rules so thick that he is essentially playing a different game than the rest of us (which is fair enough, but it makes it damn hard for us to give any meaningful advice).
*Sidenote: I did have my character die in an Earthdawn campaign many years ago because I joined late in the campaign and my GM apparently forgot that I didn't have the 'insane mystic armor bonus from an artifact' that the rest of the party got earlier, making a fairly brief jaunt into corrupted astral space quite fatal for my poor elementalist. I guess I'm trying to say there might be something weird going on that the OP isn't a part of, but that seems fairly unlikely...
At level 10, a Ranger's first Favored Enemy bonus will be +6/+6. This could also be a +3 dodge bonus to AC with the Favored Defense feat. And a +3 bonus to saves against breath weapons and fear effects, as well as the Stalwart ability [assuming you didn't pick an archetype that trades Evasion], with the Focused Dragon Expertise feat. At level 15, Favored Enemy is +8/+8, and the bonuses from the aforementioned feats increase to +4 [half your Favored Enemy bonus].
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At level 10, a Ranger's first Favored Enemy bonus will be +6/+6. This could also be a +3 dodge bonus to AC with the Favored Defense feat. And a +3 bonus to saves against breath weapons and fear effects, as well as the Stalwart ability [assuming you didn't pick an archetype that trades Evasion], with the Focused Dragon Expertise feat. At level 15, Favored Enemy is +8/+8, and the bonuses from the aforementioned feats increase to +4 [half your Favored Enemy bonus].
When facing off against what should be a TPK-level dragon, I suspect you need to take sage advice from the Waco Kid: https://www.youtube.com/watch?v=Dt-dA5gJaHU.
Seriously, if you need to pull out all the stops just to have an almost reasonable chance to hit such a foe with your first iterative attack, it's probably going to kill you long before you seriously dent its HP pool...